Chapter 15: “No” Problems: On Lojban Negation
In expressing a scalar negation, we must provide some indication of the scale, range, frame-of-reference, or universe of discourse that is being dealt with in an assertion. As stated in c15-§4, the default is the set of plausible alternatives. Thus if we say:
✥5.1 le stizu cu na'e xunre The chair is a non-(red-thing).
the pragmatic interpretation is that we mean a different color and not
✥5.2 le stizu cu dzukla be le zarci The chair walkingly-goes-to-the-market.
However, if we have reason to be more explicit (an obtuse or contrary listener, or simply an overt logical analysis), we can clarify that we are referring to a color by saying:
✥5.3 le stizu cu na'e xunre skari The chair is of a non-(red)-color (as perceived by something under some conditions).
We might also have reduced the pragmatic ambiguity by making the two trailing sumti values explicit (the “as perceived by” and “under conditions” places have been added to the place structure of “xunre”). But assume we have a really stubborn listener (an artificially semi-intelligent computer?) who will find a way to misinterpret ✥5.3 even with three specific sumti provided.
In this case, we use a sumti tagged with the sumti tcita “ci'u”, which translates roughly as “on a scale of X”, where “X” is the sumti. For maximal clarity, the tagged sumti can be bound into the negated selbri with “be”. To clarify ✥5.3, we might say:
✥5.4 le stizu cu na'e xunre be ci'u loka skari The chair is a non-(red on-a-scale-of-colorness)-thing.
We can alternately use the sumti tcita “teci'e”, based on “ciste”, which translates roughly as “of a system of components X”, for universes of discourse; in this case, we would express ✥5.3 as:
✥5.5 le stizu cu na'e xunre be teci'e le skari The chair is a non-(red of-a-system-with-components-the-colors)-thing.
Other places of “ciste” can be brought out using the grammar of selma'o BAI modals, allowing slightly different forms of expression, thus:
✥5.6 le stizu cu na'e xunre be ci'e lo'i skari The chair is a non-(red of-a-system-which-is-the-set-of-colors)-thing.
The cmavo “le'a”, also in selma'o BAI, can be used to specify a category:
✥5.7 le stizu cu na'e xunre be le'a lo'i skari The chair is a non-(red of-a-category-which-is-the-set-of-colors)-thing.
which is minimally different in meaning from ✥5.6.
The cmavo “na'e” is not the only member of selma'o NAhE. If we want to express a scalar negation which is a polar opposite, we use the cmavo “to'e”, which is grammatically equivalent to “na'e”:
✥5.8 le stizu cu to'e xunre be ci'u loka skari The chair is a (opposite-of red) on-scale a-property-of color-ness.
Likewise, the midpoint of a scale can be expressed with the cmavo “no'e”, also grammatically equivalent to “na'e”. Here are some parallel examples of “na'e”, “no'e”, and “to'e”:
✥5.9 ta melbi That is-beautiful. ✥5.10 ta na'e melbi That is-non-beautiful. That is other than beautiful. That is ugly [in one sense]. ✥5.11 ta no'e melbi That is-neutrally beautiful. That is plain/ordinary-looking (neither ugly nor beautiful). ✥5.12 ta to'e melbi That is-opposite-of beautiful. That is ugly/very ugly/repulsive.
The cmavo “to'e” has the assigned rafsi “-tol-” and “-to'e-”; the cmavo “no'e” has the assigned rafsi “-nor-” and “-no'e-”. The selbri in ✥5.10 through ✥5.12 could be replaced by the lujvo “nalmle”, “normle”, and “tolmle” respectively.
This large variety of scalar negations is provided because different scales have different properties. Some scales are open-ended in both directions: there is no “ultimately ugly” or “ultimately beautiful”. Other scales, like temperature, are open at one end and closed at the other: there is a minimum temperature (so-called “absolute zero”) but no maximum temperature. Still other scales are closed at both ends.
Correspondingly, some selbri have no obvious “to'e” — what is the opposite of a dog? — while others have more than one, and need “ci'u” to specify which opposite is meant.